Though brief, the exchange captures Gillibrand’s political skill, as she seizes on an opportunity to make a reporter feel like an insider and, at the same time, showcases cordial relations with a colleague others are casting as a potential rival.

Telegenic and brainy, the 47-year-old junior senator from New York and mother of two has become a visible face in the Senate, a regular at women’s forums and policy talk shows, and something of a political pinup (The Hill named her one of its 50 most beautiful in 2010). An obscure second-term House member when appointed to fill Clinton’s seat in 2009, she has won election and reelection, both by landslides.

“If Hillary Clinton doesn’t run in 2016, I wouldn’t be surprised to see Kirsten Gillibrand jump in,” says Larry Sabato, director of the Center for Politics at the University of Virginia. “Gillibrand seems to have the ambition to do it.”

In her sixth year in the Senate, working out of Clinton’s former quarters in the Russell Senate Office Building, Gillibrand has carved out territory including military and middle-class issues, and fashioned an image as a tenacious fighter for women. Now, she has taken another step along the modern-day passage to the presidency: writing a political memoir. With an introduction by Clinton, “Off the Sidelines: Raise Your Voice, Change the World” is due out Sept. 9. Like Gillibrand’s political action committee of the same name, it exhorts women to take the lead in politics, in business and at home. “I wrote the book to encourage women to use their voices,’’ she says.

Gillibrand says she’s “worried that the women’s movement is dead.” Acknowledging that some feminist leaders might find that characterization inflammatory, she says, “I think those of us who are in the trenches recognize we’re in a tough place.” While citing achievements such as keeping abortion-rights efforts alive and helping women advance in the workforce, she contends that “there’s no functional movement where we’re working together and making sure all women are heard on all these issues.”

With “Off the Sidelines,” she says, “I’m creating a call to … create the women’s movement we need for this generation.”

The title is “perfect for her, since she is not on the sidelines one minute of her life,” says Rep. Debbie Wasserman Schultz (D-Fla.), Gillibrand’s close friend and softball team co-captain.

So, to continue the analogy, the question becomes this: If Gillibrand is off the sidelines, where is she going? Is she headed for the quarterback position? Is she running for president?

“I would say that I’m supporting Hillary in 2016,” the senator says, “and I am going to fight very hard to see that she wins.”

And if Clinton doesn’t run?

Gillibrand shrugs.

Political books serve different purposes: campaign tools, ego boosters, policy tracts, coming-of-age reminiscences. Gillibrand’s has a bit of each. It tells the story of Kirsten Elizabeth Rutnik, a middle-class Roman Catholic Albany schoolgirl who was driven to excel and influenced by a line of strong-willed, iconoclastic women who cared little about public opinion.

Her maternal great-grandmother, Mimi, an Irish immigrant, worked at an ammunition arsenal during World War II, kicked her husband out of the house for drinking too much and chose to raise her children alone. Mimi’s daughter, Kirsten’s grandmother, Dorothea “Polly” McLean Noonan became a prominent figure in Albany and an intimate of longtime mayor Erastus Corning. Salty-tongued and brazen, she was a leader of the Albany Democratic Party machine, doling out patronage and favors, organizing government secretaries known as “Polly’s Girls,” and heading the Albany Democratic Women’s Club.

Kirsten (everyone called her Tina) learned campaign basics from her grandmother, stuffing envelopes, sticking bumper stickers on cars, handing out fliers and knocking on doors. “I really wanted to follow my grandmother into politics,” she says, “and I liked how assured she was, and I liked that she was passionate about what she did.”

Kirsten’s mother, also named Polly, founded a law firm in Albany with her husband, Douglas P. Rutnik. Polly Rutnik ran the home as well as practicing law. She cooked, did most of the housework, looked after her three children, Douglas, Kirsten and Erin, and found time to earn a black belt in karate and hunt turkeys for Thanksgiving. “She prioritized both work and family; I never imagined I would do otherwise,” Gillibrand writes in the book. (Kirsten’s parents divorced when she was 22.)

Kirsten learned to cope with stress and competition on the tennis court, and learned to argue at home, with her father. “I fought about everything,” she says. “Can I go to a party? Can I go to a concert?” He called her Foghorn and Loudmouth.

Despite standing up to her father, “I was a massive kiss-[a--] and lived for positive reinforcement,” she writes in her book. “As a child, I wrote in perfect cursive penmanship, thanks to the nuns. I did all my homework as soon as I got home, and I kept my room clean.” She was a goody-two-shoes, except for her temper and her elbows-out determination to excel. “Whatever I did — debating, playing the piano or tennis, selling Girl Scout cookies — I had to earn a gold star. ”

She went to Catholic schools from kindergarten to middle school and attended Emma Willard, an elite all-girls high school. At Dartmouth, she ignored campus politics, joined a sorority, majored in Asian studies (spending a semester in Beijing, where her roommate was Connie Britton of TV’s “Nashville,” who remains a friend) and graduated magna cum laude.Only after earning a degree at the UCLA School of Law and landing a job at the international law firm Davis Polk & Wardwell in New York City did Gillibrand get involved in politics.

“The voice that inspired me to take my life in a new direction came in a pink suit,” she writes. On Sept. 5, 1995, first lady Hillary Clinton spoke in Beijing at the Fourth World Conference on Women, forging the phrase that became a mantra for women worldwide: Human rights are women’s rights and women’s rights are human rights. Hearing about the speech made Gillibrand wish she had been there and had been part of the conversation. And it brought back her childhood dream of being in politics, like her grandmother.

Shortly afterward, Gillibrand heard Clinton speak at the Women’s Leadership Forum in New York, which she joined. “That’s what got me into the nuts and bolts of New York City politics,” Gillibrand says. In 1996, she was an unpaid fundraiser in President Bill Clinton’s reelection campaign and, four years later, volunteered to raise money for Vice President Al Gore. After Gore’s defeat, she went to work at Boies, Schiller & Flexner — whose star attorney, David Boies, had represented Gore in Bush v. Gore — and was made partner, earning about $450,000 a year.

She kept her hand in politics, fundraising for Hillary Clinton’s senatorial campaign and training to run for office herself, moving to her firm’s Albany office so she could vie for a congressional seat close to her Upstate roots. In 2006, she ran for the conservative 20th Congressional District against a popular Republican.

She proved to be a tireless campaigner and prolific fundraiser, amassing $4.6 million, a stunning sum for a congressional campaign. Her opponent, Rep. John E. Sweeney, who portrayed her as an out-of-touch, rich Manhattanite, was leading in the polls. But shortly before Election Day, a police report was leaked to newspapers saying that Sweeney’s wife had called 911 to say he was beating her. His camp said Gillibrand leaked the report; she declined to say. She won by 6 points.

Despite that upset, Gillibrand was unknown in much of New York when Gov. David A. Paterson appointed her to fill Clinton’s Senate term in a controversial move seen as a nod to her gender and Upstate support. It didn’t help that she had been the second choice, after Caroline Kennedy, yet ahead of more experienced representatives. Gillibrand was sworn in on Jan. 27, 2009, at 42 then the youngest member of the U.S. Senate.

From the start she ran into a wall. Some colleagues and newspaper columnists called her Tracy Flick, referring to the blond, ambitious Reese Witherspoon character in the film “Election.” Some older congressmen poked at her weight. “Don’t lose too much weight now. I like my girls chubby,” said one.

In New York City’s liberal circles, her 15 years as a highly paid corporate lawyer and two years representing a conservative district didn’t sit well. She was seen as a political lightweight and labeled pro-gun, pro-Wall Street, anti-immigration and pro-tobacco. (During the tobacco wars of the 1990s, she had helped represent Altria, parent company of Philip Morris.) Enlisting supporters like the Clintons, she countered with a campaign to win over blacks, Hispanics and other liberals. She won election to a Senate term in 2010, 63 to 35 percent, then reelection two years ago, 72to 26 percent.

Along with broadening her electoral base, Gillibrand has come to be associated with several high-profile issues. She was a leader in the successful struggle to repeal “don’t ask, don’t tell.” She was on the front lines of the campaign to gain approval of marriage equality in the New York legislature, and was among the first Democrats to call for bringing combat troops home from Afghanistan. To address the plight of low- and middle-income families, she has fashioned an ambitious agenda that includes raising the minimum wage, affordable day care and universal pre-K education. She established Off the Sidelines as a PAC in 2011 and raised $1 million for female candidates in the 2012 cycle. Her goal is to double that for the midterms this year, and she says she is close to doing it.

Another issue she has focused on: sexual abuses in the armed forces. She waged a yearlong battle for her bill to strip commanders of their authority to prosecute those cases and give that responsibility to military lawyers outside the chain of command. Military leaders opposed the measure, and in March, her proposal came up five votes short of the 60 needed to advance to the Senate floor. Sen. Claire McCaskill of Missouri, a Democrat, led the fight to block it, offering bipartisan reforms that kept prosecution within the chain of command.

“I was devastated,” Gillibrand says.

“She is formidable,” says McCaskill, who is now working with Gillibrand on legislation to curb sexual assaults on university campuses. “She doesn’t stop. She lobbies every senator over and over. I tell people, ‘If you are going to oppose Kirsten Gillibrand, you need to pack your lunch, because you won’t have time to go out.’ ”

Hill watchers often cite Gillibrand’s political appeal. “She has impressively emerged from the paralyzed muck of the U.S. Senate because she offers a progressive vision,” says Steve Clemons, a senior fellow at the New America Foundation and an editor at large at the Atlantic. Gillibrand “brings to her game a love of detail and dealmaking reminiscent of LBJ.”

And while Sabrina Schaeffer, executive director of the conservative Independent Women’s Forum, opposes Gillibrand’s legislative agenda, she also says Gillibrand has a “girl-next-door personality women and men can identify with” and “has checked off all the right boxes on women’s issues.”

But Michael Barone, a political analyst and resident fellow at the American Enterprise Institute and contributor to Fox News, dismisses Gillibrand, saying: “I don’t think many conservatives have given much thought to her. They see her as a conventional liberal in a safe seat with no national career in the short term.”

Gillibrand’s memoir, which she will promote on a coast-to-coast tour this month, will generate talk of a presidential run no matter how much she fends off the question.

In style, however, Gillibrand’s book differs significantly from previous political memoirs. Hers is a quick read, chatty, candid, with self-help and even diet advice. “It’s not a policy book,” she says.

Beltway commentators may find it frothy, but she says she wants to reach a wider set of readers, especially women, people who may not want an insider’s account of life in Washington. “Empowerment of all women is important,” she says, not just those who are seeking to crack the ceiling, or lean in or lean out.

She bristles at the debate about whether women can have it all. “It’s an absurd argument.” The very phrase “have it all,” she says, implies that women are greedy and demeans stay-at-home mothers. For many mothers, she says, working is a financial necessity, not a choice, and she says she is particularly concerned about low-and-middle-income women, especially single moms. “I don’t have their tough choices, but I share the same experience that they have,” she says. “We all want to be good moms. We all want to be good at our jobs. We all want to provide for our children.”

Still, if the question isn’t about having it all, many who spend time around Kirsten Gillibrand seem to wonder how she does it all. She and her husband, Jonathan Gillibrand, a British-born financial manager, moved to Washington in 2007, but for the past two years, he has spent workweeks in New York City while their two boys stay with her.

“She is taking care of two small children and working her head off in the Senate,” says Sen. Susan Collins of Maine, among the Republicans who backed Gillibrand on the military bill. “It’s not like she has live-in help the way a lot of people in the Senate do, and I just don’t know how she does it.”

Gillibrand’s mornings begin between 6 and 6:30, when Henry, her 6-year-old, a live wire who is starting first grade, wakes her. “Almost always, I feel exhausted when I get up,” she says. She fixes breakfast for the boys, packs their lunches, does laundry or dishes, checks their homework and drives them to school. If she has time she stops at the gym for a workout and arrives in her office by 9. She’s usually on Capitol Hill until late afternoon when she gets away to pick up the boys at school.

A trim 5-foot-2, she gains weight easily — 50 pounds when she was pregnant with Henry. When she got to the Senate, she went on a crash regimen, dropped her size to a 4 or 6 from 16, and was featured in Vogue. “If I eat more than 1,400 calories a day, I gain weight,” she says. She cooks almost every weeknight, typically chicken, fish or lean beef, with salad and vegetables. A master juggler, she can cook, sweep, pick up schoolbooks and children’s shoes lying about, and carry on a conversation at the same time.

After dinner, she might take Theo, who is 10 and in fifth grade, to sports practice or whatever is on his schedule. Like their mother, the boys lead busy lives: baseball, soccer, squash, T-ball, piano, singing and taekwondo. She tries to get to bed about 10. “If I don’t get enough sleep, I get irritable and emotional.”

The Gillibrands live in a three-story brick rowhouse on Capitol Hill. They have a sparsely furnished living room with an upright piano. The kitchen, a comfortable open space with a dining table, has framed photographs of the senator with the boys, Henry’s crayon drawings, and notes on the refrigerator door. Parked out back is an old Porsche belonging to Gillibrand’s husband, currently working with Formula One racing. “We use my van to get around,” she says.

The couple met in 1999 when Jonathan, two years her junior, was getting an MBA at Columbia and she was working at Davis Polk. They were married in 2001. “We’re opposites in many ways,” she says. “That’s probably why it works.” Jonathan, who is private, methodical and thoughtful, has been encouraging her political career, offering cautious advice and absorbing criticism. But her first year in the House was difficult, as she recounts in her book. They lived with Theo in a Virginia suburb. Jonathan hated Washington and had no job. They argued. At one point he told her, “Your job is the reason we don’t have more kids!” She realized he had a point. Soon she was pregnant with Henry.

When the family is together on weekends “we do things the boys like to do,’’ usually sports, she says. “Jonathan is really good about chores. I do not nag him. I do not ask him to do things. I typically do the cooking because it relaxes me. But Jonathan helps clean up. He’s is more supportive than the average husband.”

For someone who is all about women forging ahead, it may seem ironic that she takes on the majority of parenting duties. But, she says: “I think most working moms do it all. They do a lot of caregiving. They do a lot of housework. And they work full time.”

The next morning in her busy office, Henry is with her, slouching on the sofa, playing with pieces on a chessboard and trying hard to obey his mother and keep quiet.

Settling into a favorite wingback chair, Gillibrand says she wants to recruit 6 million women to active service in politics, businesses and communities. Six million is the number of women who entered the workforce to replace the men who had gone to battle during World War II.

Looking up at a poster of Rosie the Riveter, the advertising character who represented those women, Gillibrand echoes, “We can do it!”

Former New York Times editor Luisita Lopez Torregrosa is a journalist and author based in New York.

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Independent Women’s Forum’s mission is to improve the lives of Americans by increasing the number of women who value free markets and personal liberty. Sister organization of Independent Women’s Voice.